Cosmological Constant and Zeta-Function

TL;DR

This paper explores a relativistic invariant zeta-function method for calculating vacuum energy's contribution to the cosmological constant, revealing its dependence on field mass and comparing it with dimensional regularization results.

Contribution

It introduces a zeta-function approach to compute vacuum energy in a relativistically invariant way and compares it with dimensional regularization, highlighting their agreement.

Findings

Vacuum energy contribution scales with the fourth power of the field mass.

Dependence on large mass scales is only logarithmic.

Results are consistent with dimensional regularization up to finite terms.

Abstract

The relativistic invariant zeta-function approach to computation of the vacuum energy contribution to cosmological constant is discussed. It is shown that this value is determined by the fourth power of the quantized field mass, while the dependence from the large mass scale is only logarithmic. This value is compared to the result obtained in the dimensional regularization scheme which also satisfies the relativistic invariance condition, and found to be the same up to irrelevant finite terms. The consequences of the renormalization group invariance are also briefly discussed.